39 citations · 57 across the 8 of their papers we have counts for
12 papers
Lacunary hyperbolic groups with fast injectivity radius growth and enough loxodromic elements are selfless
Goulnara Arzhantseva, Martin Finn-Sell
We prove that a lacunary hyperbolic group with sufficient generics is selfless in the sense of Amrutam--Gao--Kunnawalkam Elayavalli--Patchell, provided the hyp…
Representation theory of topological full groups of étale groupoids and paradoxicality
Vadim Alekseev, Martin Finn-Sell
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full…
Controlled Analytic Properties and the Quantitative Baum-Connes Conjecture
Martin Finn-Sell
We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains m…
Unrestricted wreath products and sofic groups
Goulnara Arzhantseva, Federico Berlai, Martin Finn-Sell +1
We show that the unrestricted wreath product of a sofic group by an amenable group is sofic. We use this result to present an alternative proof of the known fact that any group ext…
Sofic boundaries of groups and coarse geometry of sofic approximations
Vadim Alekseev, Martin Finn-Sell
Sofic groups generalise both residually finite and amenable groups, and the concept is central to many important results and conjectures in measured group theory. We introduce a to…
Non-amenable principal groupoids with weak containment
Vadim Alekseev, Martin Finn-Sell
We construct examples of principal groupoids that have weak containment but are not amenable, thus answering questions by Claire Anantharaman-Delaroche and Rufus Willett.
The Asymptotic Dimension of Box Spaces for Elementary Amenable Groups
Martin Finn-Sell, Jianchao Wu
We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the…
Almost quasi-isometries and more non-exact groups
Martin Finn-Sell
We study permanence results for almost quasi-isometries, the maps arising from the Gromov construction of finitely generated random groups that contain expanders (and hence that ar…
Subsemigroup, ideal and congruence growth of free semigroups
Alex Bailey, Martin Finn-Sell, Robert Snocken
Using Rees index, the subsemigroup growth of free semigroups is investigated. Lower and upper bounds for the sequence are given and it is shown to have superexponential growth of s…
On the Baum-Connes conjecture for Gromov monster groups
Martin Finn-Sell
We present a geometric approach to the Baum-Connes conjecture with coefficients for Gromov monster groups via a theorem of Khoskham and Skandalis. Secondly, we use recent results c…
Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture
Martin Finn-Sell
The connection between the coarse geometry of metric spaces and analytic properties of topological groupoids is well known. One of the main results of Skandalis, Tu and Yu is that…
Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture
Martin Finn-Sell, Nick Wright
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove t…